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Search: id:A147301
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| A147301 |
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a(n) = smallest value of parameter m such that function rad(m n (n - m)) has maximal value n=2,3,4..., 0 < m < n where function rad(k) called also radical(k) is product distinct prime divisors of k. |
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5
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| 1, 1, 1, 2, 1, 2, 3, 2, 3, 5, 5, 6, 3, 2, 5, 7, 7, 6, 7, 10, 7, 10, 11, 11, 11, 13, 13, 14, 13, 14, 15, 14, 15, 13, 17, 15, 17, 17, 19, 19, 19, 21, 21, 22, 17, 21, 19, 23, 21, 22, 23, 23, 23, 26, 23, 26, 23, 29, 29, 30, 29, 29, 31, 31, 31, 33, 33, 34, 33, 34, 35, 35, 35, 37, 37, 38
(list; graph; listen)
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OFFSET
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2,4
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COMMENT
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Function rad(k) is used in ABC conjecture applications.
For smallest values of function rad(m n (n - m)) see A147298
For biggest values of function rad(m n (n - m)) see A147299
For numbers m for which rad(m n (n - m)) reached minimal value see A147300
For numbers m for which rad(m n (n - m)) reached maximal value see A147301
Sequence in each value Log[n]/Log[A147298(n)] reached records see A147302
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MATHEMATICA
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logmax = 0; aa = {}; bb = {}; cc = {}; dd = {}; ee = {}; ff = {}; gg \ = {}; Do[min = 10^100; max = 0; ile = 0; Do[If[GCD[m, n, n - m] == 1, ile = ile + 1; s = m n (n - m); k = FactorInteger[s]; g = 1; Do[g = g k[[p]][[1]], {p, 1, Length[k]}]; If[g > max, max = g; mmax = m]; If[g < min, min = g; mmin = m]], {m, 1, n - 1}]; AppendTo[aa, min]; AppendTo[bb, max]; AppendTo[cc, mmax]; AppendTo[dd, mmin]; AppendTo[gg, ile]; If[(Log[n]/Log[min]) > logmax, logmax = (Log[n]/Log[min]); AppendTo[ee, {N[logmax], n, mmin, min, mmax, max}]; Print[{N[logmax], n, mmin, min, mmax, max}]; AppendTo[ff, n]], {n, 2, 129}]; cc (*Artur Jasinski*)
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CROSSREFS
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A085152, A085153, A147298-A147307.
Sequence in context: A119994 A029167 A161103 this_sequence A108380 A112779 A029201
Adjacent sequences: A147298 A147299 A147300 this_sequence A147302 A147303 A147304
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008
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